US6937250B1 - System and method for mapping textures onto surfaces of computer-generated objects - Google Patents
System and method for mapping textures onto surfaces of computer-generated objects Download PDFInfo
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- US6937250B1 US6937250B1 US09/708,775 US70877500A US6937250B1 US 6937250 B1 US6937250 B1 US 6937250B1 US 70877500 A US70877500 A US 70877500A US 6937250 B1 US6937250 B1 US 6937250B1
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- texture
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- texel
- texture map
- map
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T15/00—3D [Three Dimensional] image rendering
- G06T15/04—Texture mapping
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- Computer Graphics (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Image Generation (AREA)
Abstract
Description
The eigenvector with the smallest eigenvalue is then calculated using standard methods. Multiplication of the individual colors with that eigenvector reduces the clustering problem to one dimension and allows the colors to be sorted according to their distance to a plane parallel to the cutting plane. The quantization threshold is set to the mean distance. In this way the mean color is in the cutting plane.
Second: Calculation of the new normal vector {right arrow over (n)}b from {right arrow over (n)} and the map entries b1 and b2:
{right arrow over (n)} B ={right arrow over (n)}+{right arrow over (e)} 1 b 1 +{right arrow over (e)} 2 b 2. (3)
Third: Calculation of the reflected view {right arrow over (v)}R vector from the unit view vector {right arrow over (v)} and the new normal vector {right arrow over (n)}B. The reflected view needs not to be normalized.
{right arrow over (v)} R ·|{right arrow over (n)}| 2=2·{right arrow over (n)}·({right arrow over (n)}·{right arrow over (v)})−{right arrow over (v)}·|{right arrow over (n)}| 2 (4)
Fourth: Calculation of the environment map coordinates from the reflected view vector. This is done by dividing by the largest component of the vector. The effort is comparable to the effort for the perspective correct texture coordinate generation.
A dedicated smart memory device for bump mapping, located in between the rasterizer and the TEXRAM, would maintain the high rendering speed since the modification of environment coordinates could then be done in parallel to texturing.
6. Texture Mapping
C d=(I d |k T|1)·T, (5)
where the term in parenthesis denotes a selection of Id, the shaded intensity of the pixel delivered by the rasterizer, kT, a constant taken from an internal register used to modify the same texture for different objects or 1 yielding T unmodified.
7. Environment Mapping
C=(C d |I d)+k s ·E. (6)
The selection says that the environment can be mapped directly onto the object as produced by the rasterizer.
8. Reflectance Mapping
C=(C c |I d)+R·(E|I s). (7)
The last selection permits the use of any externally generated specular intensity component Is.
C=(k a+(1−k a)·T)·D, (8)
where D is the interpolated detail map color and ka is taken from an internal register. In this way it is possible to modify the detail color with the color of the overlying texel thus to use the same detail map for differently colored regions of the texture.
where u, v are the texture coordinates and x,y are the screen addresses of the pixel
and thus,
The ellipse is defined by:
{right arrow over (x)} T(M −1)T M −1 {right arrow over (x)}=1. (12)
(M−1)TM−1 is symmetrical and can be diagonalized:
Its eigenvectors
give the directions of the main axes of the ellipse. N has the eigenvalues
We can save the calculation of M−1 if we use M−1 det (M) instead, which can be derived from M by reordering the matrix coefficients without division.
N′=N det(M)2 (16)
has the same eigenvectors as N:
{right arrow over (v)}1′={right arrow over (v)}1 and {right arrow over (v)}2′={right arrow over (v)}2, (17)
with the eigenvalues
λ1′=b2 and =λ2′=a2. (18)
The main axis of the ellipse, which we are looking for, has the direction of the eigenvector with the smaller eigenvalue.
q=min(|{right arrow over (r)} 1|,|{right arrow over (r)}2 |, d 1 ,d 2) (19)
as edge length and
rounded to the nearest power of two as the number of square mipmapped texture elements for the footprint. A difference vector Δ{right arrow over (r)}=(Δu, Δv) is constructed according to:
A sequence of sample points pn is generated by
Claims (27)
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US09/708,775 US6937250B1 (en) | 1996-07-01 | 2000-11-07 | System and method for mapping textures onto surfaces of computer-generated objects |
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US2093596P | 1996-07-01 | 1996-07-01 | |
US08/884,044 US6236405B1 (en) | 1996-07-01 | 1997-06-27 | System and method for mapping textures onto surfaces of computer-generated objects |
US09/708,775 US6937250B1 (en) | 1996-07-01 | 2000-11-07 | System and method for mapping textures onto surfaces of computer-generated objects |
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US08/884,044 Division US6236405B1 (en) | 1996-07-01 | 1997-06-27 | System and method for mapping textures onto surfaces of computer-generated objects |
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US6937250B1 true US6937250B1 (en) | 2005-08-30 |
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US08/884,044 Expired - Lifetime US6236405B1 (en) | 1996-07-01 | 1997-06-27 | System and method for mapping textures onto surfaces of computer-generated objects |
US09/708,775 Expired - Lifetime US6937250B1 (en) | 1996-07-01 | 2000-11-07 | System and method for mapping textures onto surfaces of computer-generated objects |
US11/507,071 Expired - Fee Related US7580043B2 (en) | 1996-07-01 | 2006-08-18 | Method for adding detail to a texture map |
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US08/884,044 Expired - Lifetime US6236405B1 (en) | 1996-07-01 | 1997-06-27 | System and method for mapping textures onto surfaces of computer-generated objects |
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US11/507,071 Expired - Fee Related US7580043B2 (en) | 1996-07-01 | 2006-08-18 | Method for adding detail to a texture map |
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US7580043B2 (en) | 2009-08-25 |
US20070070078A1 (en) | 2007-03-29 |
US6236405B1 (en) | 2001-05-22 |
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